OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
G.f. A(x) satisfies: A(x) = 1 + x * A(x^2/(1 - x)^2) / (1 - x).
E.g.f.: Integral exp(x) * Sum_{n>=0} a(n) * x^(2*n) / (2*n)! dx.
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 2 k] a[k], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 32}]
nmax = 32; A[_] = 0; Do[A[x_] = 1 + x A[x^2/(1 - x)^2]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 01 2022
STATUS
approved